Precalculus Examples

$8 x - (2 x + 1) = 3 x - 13$

Step 1

Simplify $8 x - (2 x + 1)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$8 x - (2 x) - 1 \cdot 1 = 3 x - 13$

Step 1.1.2

Multiply $2$ by $- 1$ .

$8 x - 2 x - 1 \cdot 1 = 3 x - 13$

Step 1.1.3

Multiply $- 1$ by $1$ .

$8 x - 2 x - 1 = 3 x - 13$

Step 1.2

Subtract $2 x$ from $8 x$ .

$6 x - 1 = 3 x - 13$

Step 2

Move all terms containing $x$ to the left side of the equation.

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Step 2.1

Subtract $3 x$ from both sides of the equation.

$6 x - 1 - 3 x = - 13$

Step 2.2

Subtract $3 x$ from $6 x$ .

$3 x - 1 = - 13$

Step 3

Move all terms not containing $x$ to the right side of the equation.

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Step 3.1

Add $1$ to both sides of the equation.

$3 x = - 13 + 1$

Step 3.2

Add $- 13$ and $1$ .

$3 x = - 12$

Step 4

Divide each term in $3 x = - 12$ by $3$ and simplify.

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Step 4.1

Divide each term in $3 x = - 12$ by $3$ .

$\frac{3 x}{3} = \frac{- 12}{3}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $3$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 12}{3}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 12}{3}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 12$ by $3$ .

$x = - 4$